Piezoresponse force microscopy (PFM) is a contact mode scanning probe microscopy (SPM) technique, which in its most basic form is used to measure out-of-plane and in-plane displacement response of ferroelectric and piezoelectric materials. For simplicity, hereinafter, the term piezoelectric will be used generally to denote materials having piezoelectric properties, including ferroelectric materials. The PFM technique is based on the reverse piezoelectric effect, where a piezoelectric material expands or contracts upon applying an electric field to the material. PFM is an example of the more general subset of SPM techniques that investigate surface motion of an actuated material that is actuated as part of the measurement technique.
PFM is described generally in Shijie Wu, Application Note: Piezoresponse Force Microscopy, Agilent Technologies (2007), which is incorporated by reference herein. In PFM, the scanning probe microscope probes a sample's mechanical response to an applied electric field. Both, contact, and non-contact techniques for PFM are known. PFM enables measurements and characterization of piezoelectric behavior of materials on the nanometer, and sub-nanometer scale. For instance, PFM can measure the electromechanical response of a material on the level of individual nanometer-scale grains. The PFM has been shown to delineate regions of different piezoresponse with sub-nanometer lateral resolution.
In PFM a micromachined probe is typically situated at the end of a cantilever. The probe tip used in PFM is usually made of, or is coated with, a conductive material, as this conductivity facilitates the electrical contact between the probe tip and the sample of material being analyzed. In contact mode PFM, an AC stimulus signal with an optional DC offset bias is applied to the probe tip, which is held in contact with the sample surface, and the piezoresponse of this sample is measured from the deflection of the cantilever using known detection techniques such as, for example, inferometry, scanning tunneling microscopy (STM) techniques, piezoelectric sensors, and optical beam techniques.
Vertical motion (i.e., perpendicular to the surface being measured), as well as lateral motion (i.e., parallel to the surface), can be detected. PFM can produce a topographic image of the surface of the sample, a piezoresponse image representing the piezoelectric properties of grains of piezoelectric material, and a phase image representing the polar orientation of the grains. PFM is particularly useful in investigating the nanometer-scale piezoelectric properties of ferroelectrics, which are the subject of intense research and development for their optoelectronic, sensor, and high-density memory applications. The lateral resolution of PFM provides highly localized information about the electromechanical behavior of thin ferroelectric films.
The amplitude and the phase of the motion are detected. This measurement technique permits the piezoresponse (PR) vector of the sample to be quantified. The displacement in the motion of the cantilever in response to PR of the sample of material is usually on the order of picometers per volt of applied AC stimulus. These displacements are detected and processed to produce the PFM measurement. Due to the very small displacements, and given the presence of electrical noise, which is unavoidably encountered in practice, conventional PFM suffers from poor signal-to-noise ratio (SNR). There are practical limits to increasing the amplitude of the AC stimulus to improve the SNR. For different materials, exceeding a certain voltage tends to re-polarize the piezoelectric domains, thereby altering the properties being measured. Accordingly, stimulation signal amplitudes must be kept low, typically necessitating the use of a lock-in amplifier. Indeed, certain materials exhibiting high re-polarization sensitivity to the stimulus signals are particularly difficult to measure using conventional techniques.
In conventional PFM techniques, the frequency of the applied AC stimulus signal has been designed to be far below the fundamental resonance frequency of the cantilever so as to avoid driving the cantilever into resonant oscillations. This is done mainly to facilitate signal processing, since the ability of the analysis system to amplify the signal representing the detected motion is determined by the signal's quality factor, Q. The Q of the contact mode measurement arrangement, with the sample being driven at a frequency far below the cantilever's first resonance, is equal to unity.
More recently, techniques based on contact resonance PFM have been developed. The contact resonance frequency is the frequency at which a system comprising a scanning probe microscope (SPM) probe in contact with an oscillating surface reaches resonance. Contact resonance PFM has been used to amplify the out-of-plane response and also to measure higher order electromechanical coefficients of ferroelectric thin film materials, thereby increasing the SNR for these measurements.
While contact mode resonance techniques offer certain advantages, they also introduce certain limitations. These include the coupling of the cantilever inertia and elastic response of the sample into the measured signal. Additionally, contact resonance characteristics include complex vibration modes, which are affected by the contact area between the probe and the sample in addition to the geometry of the cantilever itself. Accordingly, the resonant frequency and the quality factor Q of the oscillation can vary significantly from point to point on even the same sample. The result, unfortunately, is the introduction of artifacts into the PFM measurement. These effects are difficult to physically quantify and correct, and hence present challenges when interpreting contact resonance PFM data.
Moreover, certain types of PFM analyses are simply not possible using known contact resonance techniques. For instance, contact resonance typically utilizes resonant frequencies of over 100 kHz, which makes contact resonance ill-suited for measuring in-plane motion of piezoelectric domains, since the probe tip does not remain with the surface at those frequencies.
In other applications of scanning probe microscopes, such as impact mode nanomechanical analysis, in particular, techniques have been developed to amplify higher-order harmonics while suppressing the excitation signal. In Turner et al., WIPO Publication No. WO 2007/095360, various preamplifying cantilevers are described for use with dynamic analysis of nanomechanical properties in which the sample material is repeatedly struck in a tapping mode by a probe tip at the end of an indentation cantilever or actuator operating in a tapping mode at a certain excitation frequency. The impacts generate higher-order oscillations, which the preamplifying cantilever of Turner et al. aims to amplify, while suppressing the excitation frequency. While Turner et al. achieve certain kinds of mechanical preamplification using principles of resonance, their approach does not address the challenges introduced by the coupling of the sample's mechanical properties into the measurement of PFM. To the contrary, the main applications discussed in Turner et al. are specifically aimed at measuring the sample's mechanical properties. Thus, Turner et al. provides little, if any, guidance on solving the problems specific to PFM and similar applications in which a de-coupling of the sample's mechanical properties from the measurement is desired.
In view of the challenges discussed above, an in view of other challenges of enhancing PFM performance, a more effective and efficient solution is needed for improving the accuracy and sensitivity of PFM.